The global contest will award $1,000 USD to 100 artists around the world.
The prolific artist had used her works as currency to pay for her medical treatments.
The painting had previously been displayed at the Musée d’Orsay in Paris.
The Smithsonian and Speed Art Museum will jointly procure the artwork.
Sotheby’s estimates that the Ming Dynasty piece is worth between $300,000 and $500,000 USD.